Some people chose to be copinglink because trauma or mental illness causes them to want to disassociate themselves from their human/normal identity. For these people identifying as a fictional character can give them mental strength they otherwise would lack. The copinglinker draws on the attributes of the character to help them work through problems they have in their life. They can also use it as a lens through which to see and understand their mental illness, trauma, etc.
This is in contrast to a kintype, which often brings with it trauma and discomfort of its own (grief, dysphoria, etc) which has to be coped with in other ways.